Equipment as diverse as voice and data communication systems, television, radio, radar, medical imaging systems, video cameras and telescopes require filters for signal processing. The technologies used to physically realize these filters are equally diverse: passive and active components, integrated and superconductive circuits, and coupled resonant cavities. The technology of choice depends on the applications requirements and on the portion of the frequency spectrum which is of interest, such as audio, microwave, or optical.
Regardless of the filter technology, the perpetual challenge in filter design is to improve filter efficiency through improvements to filter electrical, or optical, and environmental performance, and through reductions to filter size and cost. Incorporating multiple signal paths from the input port to the output port of a filter is known as an important means of improving filter efficiency.
There are also various well-known methodologies for designing such multi-path filters to satisfy pre-determined transfer characteristic requirements. One such method is to develop a normalized coupling coefficient matrix for a single symmetric canonical filter realization, where the coupling coefficients represent the magnitude and sense (positive or negative) of the electromagnetic coupling between resonators in the signal path.
A coupling coefficient matrix m, for a six-resonator, canonical, bandpass filter is shown below, with the signal entering at resonance 1 and exiting at resonance 6, and where m.sub.x,y =m.sub.y,x (m is symmetric about its principle diagonal), and m.sub.x,y represents the coupling between resonances x and y. Typically, only the value of m.sub.2,5 is negative, so that two real frequency zeros of transmission are contributed to the filter response. Also, the magnitude of m.sub.2,5, .vertline.m.sub.2,5 .vertline., is typically about an order of magnitude smaller than the magnitudes of the other non-zero couplings. The structure is termed "canonic" because it involves the minimum number of couplings needed to achieve its level of filter performance (that is, six poles and two zeros of transmission). ##EQU1##
This matrix can then be transformed to achieve a new realization while retaining the power transfer characteristic it represents by applying successive similarity transformations of the form: EQU B=R.sub.p,q.sup.T .multidot.A.multidot.R.sub.p,q
or EQU B=R.sub.p,q .multidot.A.multidot.R.sub.p,q.sup.T
Here, R.sub.p,q is known as a plane rotation matrix, which is an identity matrix with matrix elements R.sub.p,p =R.sub.q,q =cos .theta..sub.p,q and R.sub.p,q =-R.sub.q,p =sin .theta..sub.p,q for p.noteq.q, where p and q are matrix indices and .theta..sub.p,q is defined as the rotation angle of the plane rotation matrix R.sub.p,q. A new coupling coefficient matrix M is formed by post-multiplying m by R.sub.p,q and pre-multiplying the result by R.sub.p,q.sup.T (which is the transpose of R.sub.p,q), or by post-multiplying m by R.sub.p,q.sup.T and pre-multiplying the result by R.sub.p,q (which is the transpose of R.sub.p,q.sup.T).
For example, m can be transformed from its canonical form into an "in-line" or "longitudinal" form using a plane rotation matrix R.sub.2,4 of the form: ##EQU2## where rotation angle .theta..sub.2,4 =tan.sup.-1 (m.sub.2,5 /m.sub.4,5). The new coupling coefficient matrix is EQU M=R.sub.2,4.sup.T .multidot.m.multidot.R.sub.2,4,
where ##EQU3## Note that the similarity transformation, which uses this rotation matrix and this choice of rotation angle, has resulted in the elimination of the M.sub.2,5 coupling and the creation of new M.sub.1,4 and M.sub.3,6 couplings. Here again, the couplings adjacent to the principal diagonal are all positive, while M.sub.1,4 and M.sub.3,6 are both negative and approximately an order of magnitude, or more, smaller than the other non-zero couplings. The matrix is still symmetrical about the principal diagonal.
Although it is generally acknowledged that an infinite number of different realizations of a particular transfer characteristic are possible, currently known filter synthesis and transformation techniques direct a designer to discover only a limited few of these, such as the single canonical and single longitudinal realizations mentioned above. Consequently, it has not been evident, even to experts in the field, that some more advantageous filter realizations are possible.
For example, in a certain type of six-resonance communication filter, the desirability of a particular filter realization not available from traditional design techniques is apparent. This situation will be described next.
In the microwave frequency realm, it is common to use a conductive cavity as a resonant element, with the cavity's shape and dimensions, and the locations, shapes, dielectric constants, and dimensions of dielectrics within the cavity being responsible for the cavities' resonant modes and their resonant frequencies. Enforcing various degrees of electromagnetic coupling between these resonances determines a specific signal power transfer characteristic as a function of signal frequency, so that the resonances together with the couplings form a frequency filter for the signal. Such filters with multiple signal paths are commonly known as multiple-coupled resonator waveguide filters, and have been used extensively in satellite communication systems. Initially, the cavity resonators had air dielectric interiors. More recently, improvements in the properties of certain ceramic materials have allowed the practice of partially loading the cavities with a low-loss, high dielectric constant ceramic, leading to further reductions in the size and weight of the filters.
This multiple-coupled cavity, multiple-mode dielectric resonator filter technology has been demonstrated to have significant performance and size advantages over simple cascade connected, single-mode non-dielectrically loaded waveguide cavity filter technology. However, as the number of resonant modes per cavity increases, the tuning complexity increases significantly. This efficiency/complexity trade-off has lead to dual-mode filters being more attractive than triple or higher-order mode filters in cost-sensitive, large product quantity applications. One particularly popular dielectrically loaded cavity dual-mode is the orthogonal HEH.sub.11 (EH.sub.11 .delta.) mode. Another is the TM.sub.110 mode.
In HEH.sub.11 dual-mode dielectric resonator filters, each physical resonator is comprised of a circularly cylindrical waveguide cavity containing a circularly cylindrical high dielectric constant (typically, .epsilon..sub.r .gtoreq.34), low-loss ceramic, which only partially fills the cavity, and is typically supported within the cavity with a minimum amount of low dielectric constant (typically, 1&lt;.epsilon..sub.r &lt;10), low loss dielectric material so that the axis of the cavity coincides with the axis of the ceramic. The dimensions of the cavity and the ceramic are chosen to realize two orthogonal resonances at a common frequency, typically corresponding to the center frequency of the passband of the filter.
It is conventional to introduce asymmetries into the cavity, or the ceramic, to produce the desired amount of coupling between the orthogonal modes. These asymmetries can be adjustable conductive or insulating tuning screws or members, or they can be permanent deformations such as cuts, notches, or protrusions. This coupling between the orthogonal modes of a single resonator will be termed intra-resonator coupling.
Resonant modes on physically adjacent, but separate, dual-mode resonators can be coupled together by placing the ceramics in a common cavity and adjusting the shape and dimensions and contents of the section of the cavity between the ceramics. Smaller couplings are conventionally achieved by spacing the ceramics farther apart within the cavity, or by reducing the non-conductive cross-sectional area of a portion of the inside of the cavity between adjacent ceramics, such as through the use of irises of a variety of thicknesses and shapes. These couplings can also be made adjustable through the use of any type of conductive or insulating member whose orientation, extent, or location within the section of cavity between the ceramics can be adjusted. This coupling between a resonant mode of one resonator and a resonant mode of another, physically separate, resonator will be termed inter-resonator coupling. Furthermore, although it is conventional for inter-resonator couplings to occur between parallel modes, the intervening cavity and its contents can be shaped to provide coupling between orthogonal modes as well.
Also, one must have a means for introducing and extracting a signal from the filter. For these filters, one can choose to have the signal input and output ports coupled to orthogonal modes on the same resonator, or to a mode or modes on physically separate resonators. An example of the former would be a realization of the canonical filter coupling matrix shown above, where resonances 1 and 6 would be orthogonal modes of a first dual-mode resonator, resonances 2 and 5 would be orthogonal modes of a second dual-mode resonator, and resonances 3 and 4 would be orthogonal modes of a third dual-mode resonator. An example of the latter would be a realization of the longitudinal filter coupling matrix shown above, where resonances 1 and 2 would be orthogonal modes of a first dual-mode resonator, resonances 4 and 3 would be orthogonal modes of a second dual-mode resonator, and resonances 5 and 6 would be orthogonal modes of a third dual-mode resonator.
When designed by conventional methods, the canonical dual-mode filter realization has the desirable characteristic of having relatively large inter-resonator couplings, which are also sometimes equal (m.sub.1,2, m.sub.2,3, m.sub.4,5, and m.sub.5,6 are much greater than m.sub.2,5, and, sometimes, m.sub.1,2 =m.sub.5,6 and m.sub.2,3 =m.sub.4,5), while having mostly small intra-resonator couplings (m.sub.1,6 and m.sub.2,5 are both much smaller than the inter-resonator couplings). Unfortunately, the input and output are difficult to isolate since they exist orthogonally on the same physical resonator. The maximum input-to-output isolation attainable in dual-mode filters is reported to be only about 25 to 30 dB, resulting in a significant degradation of filter stopband performance, in some applications.
The longitudinal dual-mode filter realization has significantly better input-to-output isolation, since the input and output exist in physically separate resonators, having no direct coupling between their resonant modes. However, when designed by conventional methods, the inter-resonator couplings are substantially different (m.sub.2,3 &gt;&gt;m.sub.1,4 and m.sub.4,5 &gt;&gt;m.sub.3,6) and the intra-resonator couplings m.sub.1,2,m.sub.3,4, and m.sub.5,6 are all rather large. In order to maintain reasonable filter sizes, bulkheads or plates with coupling slots known as irises are typically employed between adjacent dual-mode resonators to realize the two very different coupling magnitudes in a single space between each pair of adjacent resonators. But these coupling irises add insertion loss, decreasing filter performance, and significantly complicate the design and construction of the filters, increasing manufacturing costs. Realizing the large intra-resonator couplings can lead to increased manufacturing costs if more complicated cavity or ceramic shapes are used, and they can lead to decreased environmental stability and increased insertion loss as tuning elements, or portions of the cavity and ceramics, are brought in closer proximity to each other.
Recently, longitudinal dual-mode dielectric resonator filters without irises (designed by traditional means) have been proposed. Unfortunately, since the alternative proposed inter-resonator coupling means (metal tuning screws) only act to increase coupling between adjacent ceramics, the smallest inter-resonator couplings (i.e., m.sub.1,4 and m.sub.3,6) determine the size of the physical separation between the adjacent ceramics, and the resulting filters are intolerably large for many applications. In addition, inter-resonator coupling screws used to realize the larger couplings (m.sub.2,3 and m.sub.4,5) can easily become so large, and penetrate into the cavity so deeply, that they can create unintended couplings and resonances within the filter which can significantly distort and degrade the filter performance.
Also, in both the canonical and longitudinal designs discussed above, two of the six resonant modes are involved in as many as three couplings to other resonant modes. The tuning of these triple-coupled resonances and their couplings is significantly more difficult than the tuning of the other single- and/or double-coupled resonances and their couplings. This added complexity translates into increased manufacturing costs.
Consequently, for dual-mode bandpass filters, it is desirable for inter-resonator couplings to be as large as possible, to minimize the physical separations between adjacent resonators, or to maximize the sizes of coupling irises (or minimize the sizes and penetrations of coupling screws) in order to minimize their insertion loss degradation and allow their mechanical tolerances to be relaxed, thereby reducing their manufacturing costs. Further, it is desirable for intra-resonator couplings to be as small as possible in order to minimize insertion loss and environmental instability due to the coupling mechanisms. Also, it is desirable for inter-resonator couplings that share the same inter-resonator separation to be as nearly equal in magnitude as possible in order to facilitate simplified iris shapes (such as circular or rectangular, rather than cross- or slot-shaped) or reduced size and penetration of coupling screws, with their commensurate reductions in manufacturing costs and improvements in filter performance. In addition, it is preferable to maximize the isolation between the input and output, minimizing degradation of filter performance. And, it is desirable to minimize the maximum number of couplings to any given resonant mode in order to simplify the tuning procedure during manufacturing, and thereby reduce manufacturing costs. It is recognized that conventional filter design methodologies do not lead to designs containing a significant majority of these desirable qualities, and that, consequently, conventional dual-mode bandpass filter implementations do not embody a significant majority of these desirable qualities.